Calculate the Engineering Ultimate Tensile Strength and the maximum load in tension testing of an annealed copper specimen with an original diameter of 5 mm. Assume that the strain hardening coefficient for annealed copper is 0.50 and that the true stress at necking is 290 MPa.

Explanation:

Original diameter = 5mm

d= 0.005m. r=0.0025m

True stress (σ) = 290MPa

Coefficient of annealing copper (n)=0.5

True stress is given as force/area

σ=F/A

Ao=πr^2

Ao=1.963×10^-5m2

F=σ ×A

F=290×10^6 ×π×(0.0025)^2

F= 5694.13N

Given that

σ=Kε^n

290=Kε^0.5

n=ε=0.5 at necking

Therefore

290=K×0.5^0.5

K=410.12MPa

ε=In(Ao/A)

0.5=In(π×0.0025^2/A)

exp(0.5)=1.96×10^-5/A

A=1.96×10^-5/exp(0.5)

A= 1.2×10^-5m2

This is the new area

Then the Ultimate Tensile Stress

σ=F/A

σ=5694.13/1.2×10^-5

σ=4.75×10^8Pa

σ=475MPa

Therefore,

The ultimate tensile stress is 475MPa.

The maximum tension is

Fo/Ao=F/A

F=(Fo/Ao) ×A

F=(5694.13/1963×10^-5)×1.2×10^-5

F= 3479.99

F=3480N.

the first, second, and fifth options

when insulating materials rub against each other, they may become electrically charged . electrons , which are negatively charged, may be 'rubbed off' one material and on to the other. the material that gains electrons becomes negatively charged. the material that loses electrons is left with a positive charge.